Global sea level is an indicator of climate change1, 2, 3, as it is sensitive to both thermal expansion of the oceans and a reduction of land-based glaciers. Global sea-level rise has been estimated by correcting observations from tide gauges for glacial isostatic adjustment—the continuing sea-level response due to melting of Late Pleistocene ice—and by computing the global mean of these residual trends4, 5, 6, 7, 8, 9. In such analyses, spatial patterns of sea-level rise are assumed to be signals that will average out over geographically distributed tide-gauge data. But a long history of modelling studies10, 11, 12 has demonstrated that non-uniform—that is, non-eustatic—sea-level redistributions can be produced by variations in the volume of the polar ice sheets. Here we present numerical predictions of gravitationally consistent patterns of sea-level change following variations in either the Antarctic or Greenland ice sheets or the melting of a suite of small mountain glaciers. These predictions are characterized by geometrically distinct patterns that reconcile spatial variations in previously published sea-level records. Under the—albeit coarse—assumption of a globally uniform thermal expansion of the oceans, our approach suggests melting of the Greenland ice complex over the last century equivalent to approx0.6 mm yr-1 of sea-level rise.